Review the assigned reading, paying particularly close attention to “Why It Matters: Functions and Function Notation,” and “Lesson 8: Functions and Their Notation.” Additionally, you may find it helpful to complete the Lesson 8 Homework to prepare for this discussion.
From this week’s reading, we learn that a relationis a correspondence between an input value and an output value. Moreover, a function is a relation in which every input value corresponds to only oneoutput value.
Relations and functions come in many different forms, and many real-life concepts can be thought of in terms of relations or functions. Consider a snack vending machine, for instance. To purchase a snack, you must press buttons (input) that correspond to your desired snack (output). If you press “A1”, you may receive Peanut M&Ms. If you press “A2”, you may be the recipient of a Snickers bar. “A3” might be a bag of Barbecue Chips.
This relation between vending machine buttons and snacks that are described above can be represented by a function since every button (input value) corresponds to only one output value (snack). I could represent this function using function notation. Let S = f(b) be a function that identifies the snack, S, from a vending machine when a button, b, is pushed. Using function notation, this can be written as f(A1) = Peanut M&Ms, f(A2) = Snickers, f(A3) = Barbecue Chips, and so on.
The domain and range of this function can be represented mathematically as follows:
Domain = {A1, A2, A3, …}
Range = {Peanut M&Ms, Snickers, Barbecue Chips, …}
Note that as long as the vending machine is stocked such that every button corresponds to a single snack, the relation described above represents a function, because every input has only one output. However, if the vending machine is stocked randomly so that a variety of snacks (outputs) correspond to the same button (input), the relation no longer would represent a function. In this case, the first time that A1 is pressed, Peanut M&Ms may come out, and the second time A1 is pressed, a Kit Kat may come out. Then, f (A1) = Peanut M&Ms or f (A1) = Kit Kat. Since A1 is paired with more than one output, the relation would no longer represent a function.
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